2019MNRAS.485.4743S

We analyse a volume-limited galaxy sample from the Sloan Digital Sky Survey (SDSS) in order to study the environments of galaxies on different length-scales in the local Universe. We measure the local dimension of the SDSS galaxies on different length-scales and we find that sheets or sheet-like structures are the most prevalent pattern in the cosmic web throughout the entire range of length-scales. The abundance of sheets peaks at 30 h^–1 Mpc and they can extend up to a length-scale of 90 h^–1 Mpc. Analysing mock catalogues, we find that the sheets are non-existent beyond 30 h^–1 Mpc in the Poisson distributions. We find that the straight filaments in the SDSS galaxy distribution can extend only up to a length-scale of 30 h^–1 Mpc. Our results indicate that the environment of a galaxy exhibits a gradual transition towards a higher local dimension with increasing length-scales, finally approaching a nearly homogeneous network on large scales. We compare our findings with a semi-analytical galaxy catalogue from the Millennium Run simulation, and these findings are in fairly good agreement with the observations. We also test the effects of the number density of the sample and the cut-off in the goodness of fit, which shows that the results are nearly independent of these factors. Finally, we apply the method to a set of simulations of the segment Cox process and we find that it can characterize such distributions.